Step 1: Selling Price (SP)

Both watches are sold at the same selling price.

\( SP_1=308 \) and \( SP_2=308 \).

Total selling price \( =308+308=616 \).

Step 2: Cost Price of the first watch (12% profit)

Profit \( =12\% \).

Formula: \( CP=\dfrac{SP\times100}{100+\text{profit}} \).

\( CP_1=\dfrac{308\times100}{112} \).

\( CP_1=275 \).

Step 3: Cost Price of the second watch (12% loss)

Loss \( =12\% \).

Formula: \( CP=\dfrac{SP\times100}{100-\text{loss}} \).

\( CP_2=\dfrac{308\times100}{88} \).

\( CP_2=350 \).

Step 4: Total Cost Price

\( CP_{\text{total}}=275+350=625 \).

Step 5: Compare total CP and total SP

Total selling price \( =616 \).
Total cost price \( =625 \).

Loss \( =625-616=9 \).

Step 6: Loss percentage

\( \text{Loss\%}=\dfrac{9}{625}\times100 \).

\( \text{Loss\%}=1.44\% \).

Step 7: Convert into mixed fraction

\( 1.44\%=1\dfrac{11}{25}\% \).

Final Answer:
Overall loss \( =\boxed{1\dfrac{11}{25}\%} \).

Question

A man sells two flats at the rate of \(1.995\) lakhs each. On one flat he gains \(5\%\) and on the other flat he loses \(5\%\).

Step 1: Selling Price (SP)

Both flats have the same selling price.

\( SP_1 = 1.995 \) lakhs and \( SP_2 = 1.995 \) lakhs.

Total selling price \( = 1.995 + 1.995 = 3.99 \) lakhs.

Step 2: Cost Price of first flat (5% gain)

Formula: \( CP = \dfrac{SP \times 100}{100 + 5} \).

\( CP_1 = \dfrac{1.995 \times 100}{105} \).

\( CP_1 = 1.90 \) lakhs.

Step 3: Cost Price of second flat (5% loss)

Formula: \( CP = \dfrac{SP \times 100}{100 - 5} \).

\( CP_2 = \dfrac{1.995 \times 100}{95} \).

\( CP_2 = 2.10 \) lakhs.

Step 4: Total Cost Price

\( CP_{\text{total}} = 1.90 + 2.10 = 4.00 \) lakhs.

Step 5: Find profit or loss

Total cost price \( = 4.00 \) lakhs.
Total selling price \( = 3.99 \) lakhs.

Loss \( = 4.00 - 3.99 = 0.01 \) lakh.

Step 6: Loss percentage

\( \text{Loss\%} = \ dfrac {0.01}{4.00} \times 100 \).

\( \text{Loss\%} = 0.25\% \).

Final Answer:
Overall loss \( = \boxed{0.25\%} \).

Question

A man sells two commodities for \(4000\) each, and overall he neither gains nor loses. If one commodity is sold at a gain of \(25\%\), find the loss percent on the other commodity.

Step 1: Selling Price

Both commodities have the same selling price.

\( SP_1 = 4000 \) and \( SP_2 = 4000 \).

Total selling price \( = 4000 + 4000 = 8000 \).

Since there is neither gain nor loss, total cost price \( = 8000 \).

Step 2: Cost Price of first commodity (25% gain)

Formula: \( CP = \dfrac{SP \times 100}{100 + 25} \).

\( CP_1 = \dfrac{4000 \times 100}{125} \).

\( CP_1 = 3200 \).

Step 3: Cost Price of second commodity

Total cost price \( = 8000 \).

\( CP_2 = 8000 - 3200 = 4800 \).

Step 4: Loss on second commodity

Selling price \( = 4000 \).
Cost price \( = 4800 \).

Loss \( = 4800 - 4000 = 800 \).

Step 5: Loss percentage

\( \text{Loss\%} = \dfrac{800}{4800} \times 100 \).

\( \text{Loss\%} = 16\dfrac{2}{3}\% \).

Final Answer:
Loss on the second commodity \( = \boxed{16\dfrac{2}{3}\%} \).

Question

A house and a shop were sold for ₹1 lakh each. The house sale resulted in a loss of \(20\%\) and the shop sale resulted in a profit of \(20\%\). Find the overall gain or loss.

Step 1: Selling Price

Selling price of house = \(1\) lakh

Selling price of shop = \(1\) lakh

Total selling price = \(1 + 1 = 2\) lakhs

Step 2: Cost Price of house (20% loss)

\( CP = \dfrac{SP \times 100}{100 - 20} \)

\( CP_{\text{house}} = \dfrac{1 \times 100}{80} = 1.25 \)

Cost price of house = 1.25 lakhs

Step 3: Cost Price of shop (20% profit)

\( CP = \dfrac{SP \times 100}{100 + 20} \)

\( CP_{\text{shop}} = \dfrac{1 \times 100}{120} = 0.8333 \)

Cost price of shop = 0.8333 lakhs

Final Answer

Overall loss = \( \dfrac{1}{12} \) lakh

Question

A man sells two articles at ₹99 each. He gains \(10\%\) on one article and loses \(10\%\) on the other. Find the overall gain or loss.

Step 1: Selling Price

Selling price of first article = \(99\)

Selling price of second article = \(99\)

Total selling price = \(99 + 99 = 198\)

Step 2: Cost Price of first article (10% gain)

Formula: \( CP = \dfrac{SP \times 100}{100 + 10} \)

\( CP_1 = \dfrac{99 \times 100}{110} = 90 \)

Step 3: Cost Price of second article (10% loss)

Formula: \( CP = \dfrac{SP \times 100}{100 - 10} \)

\( CP_2 = \dfrac{99 \times 100}{90} = 110 \)

Step 4: Total Cost Price

Total cost price \( = 90 + 110 = 200 \)

Step 5: Profit or Loss

Total selling price = \(198\)

Total cost price = \(200\)

Loss \( = 200 - 198 = 2 \)

Final Answer

Overall loss = ₹\(2\)

Correct option: (c)

Question

A man sold two steel chairs for ₹500 each. On one chair, he gained \(20\%\) and on the other chair, he lost \(12\%\). Find the overall gain or loss percentage.

Step 1: Selling Price

Selling price of first chair = \(500\)

Selling price of second chair = \(500\)

Total selling price = \(500 + 500 = 1000\)

Step 2: Cost Price of first chair (20% gain)

Formula: \( CP = \dfrac{SP \times 100}{100 + 20} \)

\( CP_1 = \dfrac{500 \times 100}{120} = 416.67 \)

Step 3: Cost Price of second chair (12% loss)

Formula: \( CP = \dfrac{SP \times 100}{100 - 12} \)

\( CP_2 = \dfrac{500 \times 100}{88} = 568.18 \)

Step 4: Total Cost Price

Total cost price \( = 416.67 + 568.18 = 984.85 \)

Step 5: Profit

Total selling price = \(1000\)

Total cost price = \(984.85\)

Profit \( = 1000 - 984.85 = 15.15 \)

Step 6: Profit Percentage

\( \text{Profit\%} = \dfrac{15.15}{984.85} \times 100 \)

\( \text{Profit\%} \approx 1.5\% \)

Final Answer

Overall gain = \( \boxed{1.5\%} \)

Question

Ranjan purchased \(120\) tables at a price of ₹\(110\) per table. He sold:

• \(30\) tables at a profit of ₹\(12\) per table
• \(75\) tables at a profit of ₹\(14\) per table
• Remaining tables at a loss of ₹\(7\) per table

Find the average profit per table.

Step 1: Total number of tables

Total tables purchased = \(120\)

Tables sold at profit/loss:

Remaining tables \( = 120 - (30 + 75) = 15 \)

Step 2: Calculate total profit

Profit on \(30\) tables \( = 30 \times 12 = 360 \)

Profit on \(75\) tables \( = 75 \times 14 = 1050 \)

Loss on \(15\) tables \( = 15 \times 7 = 105 \)

Step 3: Net profit

Total profit \( = 360 + 1050 = 1410 \)

Net profit \( = 1410 - 105 = 1305 \)

Step 4: Average profit per table

Average profit \( = \dfrac{1305}{120} \)

\( = 10.875 \)

Final Answer

Average profit per table \( = \boxed{₹10.875} \)

Correct option: (b)

Question

Sanket purchased \(20\) dozen notebooks at ₹\(48\) per dozen. He sold \(8\) dozen at a profit of \(10\%\) and the remaining \(12\) dozen at a profit of \(20\%\). Find his overall profit percentage.

Step 1: Total Cost Price

Cost price per dozen = \(48\)

Total dozens purchased = \(20\)

Total cost price \( = 20 \times 48 = 960 \)

Step 2: Selling price of 8 dozen (10% profit)

Selling price per dozen \( = 48 \times \dfrac{110}{100} = 52.8 \)

Selling price of 8 dozen \( = 8 \times 52.8 = 422.4 \)

Step 3: Selling price of 12 dozen (20% profit)

Selling price per dozen \( = 48 \times \dfrac{120}{100} = 57.6 \)

Selling price of 12 dozen \( = 12 \times 57.6 = 691.2 \)

Step 4: Total Selling Price

Total selling price \( = 422.4 + 691.2 = 1113.6 \)

Step 5: Profit

Profit \( = 1113.6 - 960 = 153.6 \)

Step 6: Profit Percentage

Profit percentage \( = \dfrac{153.6}{960} \times 100 \)

\( = 16\% \)

Final Answer

Overall profit percentage \( = \boxed{16\%} \)

Correct option: (c)

Question

Hemant sold \(10\) sarees for a total profit of ₹\(460\) and \(12\) sarees for a total profit of ₹\(144\). At what profit per saree should he sell the remaining \(20\) sarees so that he gets an average profit of ₹\(18\) per saree?

Step 1: Total number of sarees

Total sarees \( = 10 + 12 + 20 = 42 \)

Step 2: Total profit required

Average profit per saree = ₹\(18\)

Total profit required \( = 42 \times 18 = 756 \)

Step 3: Profit already earned

Profit on \(10\) sarees = ₹\(460\)

Profit on \(12\) sarees = ₹\(144\)

Total profit earned \( = 460 + 144 = 604 \)

Step 4: Profit required on remaining 20 sarees

Remaining profit \( = 756 - 604 = 152 \)

Step 5: Profit per saree

Profit per saree \( = \dfrac{152}{20} = 7.6 \)

Final Answer

Required profit per saree \( = \boxed{₹7.60} \)

Correct option: (b)

Question

In a shop, \(80\%\) of the articles are sold at a profit of \(10\%\) and the remaining articles are sold at a loss of \(40\%\). Find the overall profit or loss.

Step 1: Assume total articles

Let total articles = \(100\)

Articles sold at profit = \(80\)

Articles sold at loss = \(20\)

Step 2: Assume cost price

Let cost price per article = \(100\)

Total cost price = \(100 \times 100 = 10000\)

Step 3: Profit on 80 articles (10% profit)

Selling price per article \( = 100 + 10\% \text{ of } 100 = 110 \)

Total selling price of 80 articles \( = 80 \times 110 = 8800 \)

Total cost price of 80 articles \( = 80 \times 100 = 8000 \)

Profit \( = 8800 - 8000 = 800 \)

Step 4: Loss on 20 articles (40% loss)

Selling price per article \( = 100 - 40\% \text{ of } 100 = 60 \)

Total selling price of 20 articles \( = 20 \times 60 = 1200 \)

Total cost price of 20 articles \( = 20 \times 100 = 2000 \)

Loss \( = 2000 - 1200 = 800 \)

Step 5: Overall result

Total profit = \(800\)

Total loss = \(800\)

Net profit/loss \( = 800 - 800 = 0 \)

Final Answer

There is no profit and no loss.

Correct option: (d)